Thread by @MBKplus

Have questions about the high-redshift galaxies that are just popping up one after the other in #JWST data and how they relate to the expansion of the Universe, expansion speeds, etc.? Here's my take, starting with a update of my plot from last week (it's hard to keep up!).

One helpful tool is a space-time diagram. The horizontal axis here shows the "comoving radial distance"; this distance is unchanging over time for galaxies that simply travel with the expansion of the Universe. The vertical axis shows time since the big bang.

I've labeled some important portions of the diagram: the black curve shows the past light cone, which is the set of points whose light is just reaching us today. That is, everything we see right now lies on the past light cone (the black line).

The "event horizon" is equivalent to our past lightcone in the infinite future: it defines everything that has been visible in the past or will ever be visible at some point in the future (gray curve). This may be a familiar concept if you've read about black holes.

Points to the left/below the past light cone have sent light that has already reached us. Points to the right/above the event horizon are unobservable even if we wait infinitely long. And points in the intermediate gray region will be observable at some point in the future.

We can put observable galaxies on the plot to make things more concrete: the stars in this plot show where galaxies at a variety of redshifts intersect with the past light cone. Today, those galaxies are at a distance that is equal to their comoving radial distance.

You can also compute how far the galaxies were away from us when their light was emitted by dividing the comoving radial distance by (1+z_galaxy).

For example, the dark orange point is a galaxy at z=4; it's now ~23 billion light years away from us, and when the light reaching us today was emitted, it was ~4.5 billion light years away.

Remember that galaxies moving with the expansion have fixed radial comoving distances? That means that they trace out vertical lines on this plot.

Notice that after galaxies emit their light that we'll receive today, they move into the region that will still be observable at some point in the future and eventually cross into the regime that is unobservable.

Taking the orange star at z=4 again: future Earth-based observers will be able to see light emitted from that galaxy until z~0.7, but any light that galaxy emits after z~0.7 will never reach Earth.

This is more extreme for higher-redshift sources: for the cyan star at z=15 (is this now considered intermediate redshift?!?), we see that we'll never be able to see light it emitted after z=2.

The last piece of the puzzle is how fast those galaxies are receding as a function of time. In this plot, points within the Hubble radius, d_H=c/H(z), lie in the blue shaded region and are receding at velocities slower than the speed of light. Points outside of d_H have v > c.

The magnenta star (z=1) lies within d_H at the time its light was emitted, meaning it was moving away from us slower than the speed of light when its light was emitted.

But notice that at earlier times, the vertical magenta line is outside of the blue region: at early times, that galaxy was receding from us faster than the speed of light. You can also see that in the future, that will happen again!

Now look at the orange and cyan stars: their world lines NEVER intersect the blue shaded region. This means that they have always been, and will always be, receding from us at a velocity faster than the speed of light!

But, because the expansion was slowing down for most of cosmic history, the light was able to make its way to us eventually. So weird! And yet, pretty straightforward to see on a plot like this.

The Hubble sphere grows with time until reaching a maximum size at z~0.6 -- this is when dark energy cause the Universe's expansion to switch from decelerating to accelerating.

The world line that intersects the Hubble sphere at this transition point is shown in black here, and it intersects the past light cone at z~1.8. That means that every galaxy we observe today with z > 1.8 is and always has been receding from us faster than the speed of light!

As emphasized there and in the nice threads from @astrokatie and @mpoessel last week, all of this is fully consistent with General Relativity and the idea that no information is transmitted faster than the speed of light (this is a mandatory disclaimer on all threads like this).

Understanding the expanding Universe and its implications for what we see is pretty mind-bending, but also pretty awesome! If you'd like a more in-depth & technical take, I highly recommend Davis & Lineweaver. If you made it this far, thanks for reading! ui.adsabs.harvard.edu/abs/2004PASA..…